The sum of some terms of G. P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

Options

A. last term = 150 and number of terms = 5
B. last term = 159 and number of terms = 7
C. last term = 161 and number of terms = 7
D. last term = 160 and number of terms = 6

Answer

D

Explanation

Let there are n terms in the given G.P. First term a = 5 and common ratio r = 2
`because` Given that sum fo n terms = 315
`rArr" " (a(r^(n) - 1))/(r - 1) = 315`
`rArr" "(5(2^(n) - 1))/(2 - 1) = 315 " " rArr " " 2^(n) - 1 = (315)/(5) = 63`
`rArr" " 2^(n) = 63 + 1 = 64 = (2)^(6)`
`rArr" " n = 6`
Then 6th term of G.P. `= ar^(5)`
`= 5 xx (2)^(5) xx 32 = 160`
Therefore, last term = 160 and number of terms = 6